We report voltage-clamp measurements through single conical nanopore obtained by chemical etching of a single ion-track in polyimide film. Special attention is paid on the pink noise of the ionic current (i.e. $1/f$ noise) measured with different filling liquids. The relative pink noise amplitude is almost independent of concentration and pH for KCl solutions, but varies strongly using ionic liquids. In particular we show that depending on the ionic liquid, the transport of charge carriers is strongly facilitated (low noise and higher conductivity than in the bulk) or jammed. These results show that the origin of the pink noise can be ascribed neither to fluctuations of the pore geometry nor to the pore wall charges but rather to a cooperative effect on ions motion.
Using a variational field theory, we show that an electrolyte confined to a neutral cylindrical nanopore traversing a low dielectric membrane exhibits a first-order ionic liquid-vapor pseudo-phase-transition from an ionic-penetration "liquid" phase to an ionic-exclusion "vapor" phase, controlled by nanopore-modified ionic correlations and dielectric repulsion. For weakly charged nanopores, this pseudotransition survives and may shed light on the mechanism behind the rapid switching of nanopore conductivity observed in experiments.
Extracting the sequence information of DNA from the blocked ionic current is the crucial step of the ionic current-based nanopore sequencing approaches. The thinnest graphene nanopore, which contained only one layer of carbon atoms, potentially has ultra-high DNA sequencing sensitivity. However, the dynamical translocation information of DNA contained in the blocked ionic current has not been well understood to date. In this letter, an assessment to the sensitivity of ionic current-based graphene nanopore DNA sensing approach was carried out using molecular dynamics simulations. By filtering t…
Bipolar nanopores have powerful rectification properties due to the asymmetry in the charge pattern on the wall of the nanopore. In particular, bipolar nanopores have positive and negative surface charges along the pore axis. Rectification is strong if the radius of the nanopore is small compared to the screening length of the electrolyte so that both cations and anions have depletion zones in the respective regions. The depths of these depletion zones is sensitive to sign of the external voltage. In this work, we are interested in the effect of the presence of strong ionic correlations (both …
Understanding the dynamics of ions in nanopores is essential for applications ranging from single-molecule detection to DNA sequencing. We show both analytically and by means of molecular dynamics simulations that under specific conditions ion-ion interactions in nanopores lead to the phenomenon of ionic Coulomb blockade, namely the build-up of ions inside a nanopore with specific capacitance impeding the flow of additional ions due to Coulomb repulsion. This is the counterpart of electronic Coulomb blockade observed in mesoscopic systems. We discuss the analogies and differences with the elec…
Ionic transport in nanopores or nanochannels is key to many cellular processes and is now being explored as a method for DNA/polymer sequencing and detection. Although apparently simple in its scope, the study of ionic dynamics in confined geometries has revealed interesting new phenomena that have an almost one-to-one correspondence with the quantum regime. The picture that emerges is that ions can form two `quasi-particle' states, one in which they surround themselves with other ions of opposite charge - ionic atmosphere - and one in which semi-bound water molecules form layers at different …
Fundamental understanding of ionic transport at the nanoscale is essential for developing biosensors based on nanopore technology and new generation high-performance nanofiltration membranes for separation and purification applications. We study here ionic transport through single putatively neutral hydrophobic nanopores with high aspect ratio (of length L=6 μm with diameters ranging from 1 to 10 nm) and with a well controlled cylindrical geometry. We develop a detailed hybrid mesoscopic theoretical approach for the electrolyte conductivity inside nanopores, which considers explicitly ion adve…
We investigate the ionic current modulation in DNA nanopore translocation setups by numerically solving the electrokinetic mean-field equations for an idealized model. Specifically, we study the dependence of the ionic current on the relative length of the translocating molecule. Our simulations show a significantly smaller ionic current for DNA molecules that are shorter than the pore at low salt concentrations. These effects can be ascribed to the polarization of the ion cloud along the DNA that leads to an opposing electric dipole field. Our results for DNA shine light on the observed discr…
The number of precise conductance measurements in nanopores is quickly growing. In order to clarify the dominant mechanisms at play and facilitate the characterization of such systems for which there is still no clear consensus, we propose an analytical approach to the ionic conductance in nanopores that takes into account (i) electro-osmotic effects, (ii) flow slip at the pore surface for hydrophobic nanopores, (iii) a component of the surface charge density that is modulated by the reservoir $p$H and salt concentration $c_s$ using a simple charge regulation model, and (iv) a fixed surface ch…
Using molecular dynamics simulations, we show that, when subject to a periodic external electric field, a nanopore in ionic solution acts as a capacitor with memory (memcapacitor) at various frequencies and strengths of the electric field. Most importantly, the hysteresis loop of this memcapacitor shows both negative and diverging capacitance as a function of the voltage. The origin of this effect stems from the slow polarizability of the ionic solution due to the finite mobility of ions in water. We develop a microscopic quantitative model which captures the main features we observe in the si…
We characterize the role of electrostatic fluctuations on the charge selectivity of cylindrical nanopores confining electrolyte mixtures. To this end, we develop an extended one-loop theory that can account for correlation effects induced by the surface charge, nanoconfinement of the electrolyte, and interfacial polarization charges associated with the low permittivity membrane. We validate the quantitative accuracy of the theory by comparisons with previously obtained Monte-Carlo simulation data from the literature, and scrutinize in detail the underlying forces driving the ionic selectivity …
Ionic currents accompanying DNA translocation strongly depend on molarity of the electrolyte solution and the shape and surface charge of the nanopore. By means of the Poisson-Nernst-Planck equations it is shown how conductance is modulated by the presence of the DNA intruder and as a result of competing electrostatic and confinement factors. The theoretical results reproduce quantitatively the experimental ones and are summarized in a conductance diagram that allows distinguishing the region of reduced conductivity from the region of enhanced conductivity as a function of molarity and the por…
Nanopores in solid state membranes are a tool able to probe nanofluidic phenomena or can act as a single molecular sensor. They also have diverse applications in filtration, desalination or osmotic power generation. Many of these applications involve chemical, or hydrostatic pressure differences, which act on both the supporting membrane and the ion transport through the pore. By using pressure differences between the sides of the membrane, and an alternating current approach to probe ion transport, we investigate two distinct physical phenomena: the elastic deformation of the membrane through…
There has been tremendous experimental progress in the last decade in identifying the structure and function of biological pores (ion channels) and fabricating synthetic pores. Despite this progress, many questions still remain about the mechanisms and universal features of ionic transport in these systems. In this paper, we examine the use of nanopores to probe ion transport and to construct functional nanoscale devices. Specifically, we focus on the newly predicted phenomenon of quantized ionic conductance in nanopores as a function of the effective pore radius - a prediction that yields a p…
Single nanopores have attracted much scientific interest due to their versatile applications. The majority of experiments have been performed with nanopores being in contact with the same electrolyte on both sides of the membrane, while solution gradients across semi-permeable membranes are omnipresent in natural systems. In this manuscript, we studied ionic and fluidic movement through thin nanopores under viscosity gradients both experimentally and using simulations. Ionic current rectification was observed under these conditions, due to solutions with different conductivities filled across …
Traditionally, ion-selectivity in nanopores and nanoporous membranes is understood to be a consequence of Debye overlap, in which the Debye screening length is comparable to the nanopore radius somewhere along the length of the nanopore(s). This criterion sets a significant limitation on the size of ion-selective nanopores, as the Debye length is on the order of 1 - 10 nm for typical ionic concentrations. However, the analytical results we present here demonstrate that surface conductance generates a dynamical selectivity in ion transport, and this selectivity is controlled by so-called Dukhin…
We present a modeling study of a nanopore-based transistor computed by a mean-field continuum theory (Poisson-Nernst-Planck, PNP) and a hybrid method including particle simulation (Local Equilibrium Monte Carlo, LEMC) that is able to take ionic correlations into account including finite size of ions. The model is composed of three regions along the pore axis with the left and right regions determining the ionic species that is the main charge carrier, and the central region tuning the concentration of that species and, thus, the current flowing through the nanopore. We consider a model of smal…
We predict streaming current inversion with multivalent counterions in hydrodynamically driven polymer translocation events from a correlation-corrected charge transport theory including charge fluctuations around mean-field electrostatics. In the presence of multivalent counterions, electrostatic many-body effects result in the reversal of the DNA charge. The attraction of anions to the charge-inverted DNA molecule reverses the sign of the ionic current through the pore. Our theory allows for a comprehensive understanding of the complex features of the resulting streaming currents. The underl…
Ionic transport in nanopores is a fundamentally and technologically important problem in view of its occurrence in biological processes and its impact on novel DNA sequencing applications. Using microscopic calculations, here we show that ion transport may exhibit strong nonlinearities as a function of the pore radius reminiscent of the conductance quantization steps as a function of the transverse cross section of quantum point contacts. In the present case, however, conductance steps originate from the break up of the hydration layers that form around ions in aqueous solution. Once in the po…
We employ a field-theoretical variational approach to study the behavior of ionic solutions in the grand canonical ensemble. To describe properly the hardcore interactions between ions, we use a cutoff in Fourier space for the electrostatic contribution of the grand potential and the Carnahan-Starling equation of state with a modified chemical potential for the pressure one. We first calibrate our method by comparing its predictions at room temperature with Monte Carlo results for excess chemical potential and energy. We then validate our approach in the bulk phase by describing the classical …
A previously developed field-theoretic model [R.D. Coalson et al., J. Chem. Phys. 102, 4584 (1995)] that treats core collisions and Coulomb interactions on the same footing is investigated in order to understand ion size effects on the partition of neutral and charged particles at planar interfaces and the ionic selectivity of slit nanopores. We introduce a variational scheme that can go beyond the mean-field (MF) regime and couple in a consistent way pore modified core interactions, steric effects, electrostatic solvation and image-charge forces, and surface charge induced electrostatic poten…
Using the hypernetted-chain/mean spherical approximation (HNC/MSA) integral equations we study the electrical double layer inside and outside a model charged cylindrical vesicle (nanopore) immersed into a primitive model macroions solution, so that the macroions are only present outside the nanopore, i.e., the vesicle wall is impermeable only to the external macroions. We calculate the ionic and local linear charge density profiles inside and outside the vesicle, and find that the correlation between the inside and outside ionic distributions causes the phenomena of overcharging (also referred…
A field theoretic variational approach is introduced to study ion penetration into water-filled cylindrical nanopores in equilibrium with a bulk reservoir. It is shown that (i) an ion located in a neutral pore undergoes two opposing mechanisms: the deformation of its surrounding ionic cloud of opposite charge, with respect to the reservoir, which increases the surface tension and tends to exclude ions form the pore, and (ii) the attractive contribution to the ion self-energy of the repulsive image forces associated with the dielectric jump between the solvent and the pore wall, which becomes m…
We model and simulate a nanopore sensor that selectively binds analyte ions. This binding leads to the modulation of the local concentrations of the ions of the background electrolyte (KCl), and, thus, to the modulation of the ionic current flowing through the pore. The nanopore's wall carries a bipolar charge pattern with a larger positive buffer region determining the anions as the main charge carriers and the smaller negative binding region containing binding sites. This charge pattern proved to be an appropriate one as shown by a previous comparative study of varying charge patterns (Mádai…
The translocation of double-stranded DNA through a solid-state nanopore may either decrease or increase the ionic current depending on the ionic concentration of the surrounding solution. Below a certain crossover ionic concentration, the current change inverts from a current blockade to current enhancement. In this paper, we show that the crossover concentration for bundled DNA nanostructures composed of multiple connected DNA double-helices is lower than that of double-stranded DNA. Our measurements suggest that counterion mobility in the vicinity of DNA is reduced depending on the three-dim…
In this paper, we present a molecular theory analysis of ions and potential distribution, degree of ionization of polyelectrolyte (PE) brushes, velocity profile, volumetric flow rate, ionic selectivity, ionic conduction and advection by electroosmotic flow in poly-acid (PA)/poly-base (PB) grafted nanopores. The generated conformations by the Rotational Isomeric State model are used in performing the minimization of the free energy functional of the system including the effects of the Born energy arising from the variation of permittivity, pH of the electrolyte, grafting density of weak PE brus…
We calculate the power spectrum of electric-field-driven ion transport through cylindrical nanometer-scale pores using both linearized mean-field theory and Langevin dynamics simulations. With the atom-sized cutoff radius as the only fitting parameter, the linearized mean-field theory accurately captures the dependence of the simulated power spectral density on the pore radius and the applied electric field. Remarkably, the linearized mean-field theory predicts a plateau in the power spectral density at low frequency $ω$, which is confirmed by the Langevin dynamics simulations at low ion conce…
Ion transport through nanopores permeates through many areas of science and technology, from cell behavior to sensing and separation to catalysis and batteries. Two-dimensional materials, such as graphene, molybdenum disulfide (MoS$_2$), and hexagonal boron nitride (hBN), are recent additions to these fields. Low-dimensional materials present new opportunities to develop filtration, sensing, and power technologies, encompassing ion exclusion membranes, DNA sequencing, single molecule detection, osmotic power generation, and beyond. Moreover, the physics of ionic transport through pores and con…
Ion transporters in Nature exhibit a wealth of complex transport properties such as voltage gating, activation, and mechanosensitive behavior. When combined, such processes result in advanced ionic machines achieving active ion transport, high selectivity, or signal processing. On the artificial side, there has been much recent progress in the design and study of transport in ionic channels, but mimicking the advanced functionalities of ion transporters remains as yet out of reach. A prerequisite is the development of ionic responses sensitive to external stimuli. In the present work, we repor…
Ion transport in extremely narrow nanochannels has gained increasing interest in recent years due to its unique physical properties, and the technological advances that allow us to study them. It is tempting to approach this regime with the tools and knowledge developed for wider microfluidic devices and use continuum models like the Poisson-Nernst-Planck equation. However, it turns out that some of the most basic principles we take for granted in a large system, such as electroneutrality, can breakdown under extreme confinement. We show that in a truly one-dimensional system, interacting with…
Based on the capillary pore model (space-charge theory) for combined fluid and ion flow through cylindrical nanopores or nanotubes, we derive the continuum equations modified to include wall slip. We focus on the ionic conductance and streaming conductance, cross-coefficients of relevance for electrokinetic energy conversion and electro-osmotic pumping. We combine the theory with a Langmuir-Stern 1-pK charge regulation boundary condition resulting in a non-monotonic dependence of the cross-coefficients on salt concentration.
We use Metropolis Monte Carlo and umbrella sampling to calculate the free energies of interaction of two methane molecules and their charged derivatives in cylindrical water-filled pores. Confinement strongly alters the interactions between the nonpolar solutes, and completely eliminates the solvent separated minimum (SSM) that is seen in bulk water. The free energy profiles show that the methane molecules are either in contact or at separations corresponding to the diameter and the length of the cylindrical pore. Analytic calculations that estimate the entropy of the solutes, which are solvat…
Ultrathin membranes have drawn much attention due to their unprecedented spatial resolution for DNA nanopore sequencing. However, the high translocation velocity (3000-50000 nt/ms) of DNA molecules moving across such membranes limits their usability. To this end, we have introduced a viscosity gradient system based on room-temperature ionic liquids (RTILs) to control the dynamics of DNA translocation through a nanometer-size pore fabricated in an atomically thin MoS2 membrane. This allows us for the first time to statistically identify all four types of nucleotides with solid state nanopores. …
Porous graphene has high mechanical strength and atomic layer thickness, which make it a promising material for material separation and biomolecule sensing. Electrostatic interactions between charges in aqueous solution are a kind of strong long-range interaction which may have great influence on the fluid transport through nanopores. Here, molecular dynamics simulations were conducted to investigate ion and water transport through a 1.05-nm-in-diameter monolayer graphene nanopore with its edge charge-modified. From the results, it is found that the nanopores are selective to counterions when …
Rectification properties of conically shaped nanopores: consequences of miniaturization
TU Darmstadt（达姆施塔特工业大学）；University of Vienna（维也纳大学）；Materials Science, TU Darmstadt（达姆施塔特工业大学材料科学系）；Department of Physics and Astronomy, University of California, Irvine（加州大学欧文分校物理与天文系）；GSI Helmholtz Center（德国重离子研究中心）
Double-stranded DNA translocates through sufficiently large nanopores either in a linear, single-file fashion or in a folded hairpin conformation when captured somewhere along its length. We show that the folding state of DNA can be controlled by changing the electrolyte concentration, pH and PEG content of the measurement buffer. At 1 M LiCl or 0.35 M KCl in neutral pH, single-file translocations make up more than 90% of the total. We attribute the effect to the onset of electroosmotic flow from the pore at low ionic strength. Our hypothesis on the critical role of flows is supported by the p…
We investigate a model nanopore sensor that is able to detect analyte ions that are present in the electrolyte solution in very small concentrations. The nanopore selectively binds the analyte ions with which the local concentrations of the ions of the background electrolyte (KCl), and, thus, the ionic current flowing through the pore is changed. Analyte concentration can be determined from calibration curves. In our previous study (Mádai et al. J. Chem. Phys., 147(24):244702, 2017.), we proposed a symmetric model (surface charge is negative all along the pore). The mechanism of sensing was a …
Modification of surface properties by polymer adsorption is a widely used technique to tune interactions in molecular experiments such as nanopore sensing. Here, we investigate how the ionic current noise through solid-state nanopores reflects the adsorption of short, neutral polymers to the pore surface. The power spectral density of the noise shows a characteristic change upon adsorption of polymer, the magnitude of which is strongly dependent on both polymer length and salt concentration. In particular, for short polymers at low salt concentrations no change is observed, despite verificatio…
Engineering the synthetic nanopores through lipid bilayer membrane to access the interior of a cell is a long persisting challenge in biotechnology. Here, we demonstrate the stability and dynamics of a tile-based 6-helix DNA nanotube (DNT) embedded in POPC lipid bilayer using the analysis of 0.2 microsecond long equilibrium MD simulation trajectories. We observe that the head groups of the lipid molecules close to the lumen cooperatively tilt towards the hydrophilic sugar-phosphate backbone of DNA and form a toroidal structure around the patch of DNT protruding in the membrane. Further, we exp…
Electrical conductivity is an inherent property of a hydrophobic porous media (HPM) and has critical applications. This research aims to provide a solution for predicting the electrical conductivity of nanoscale HPM with heterogeneous pore structure. Molecular dynamics (MD) simulations are compared with the modified Poisson-Boltzmann (MPB) model for understanding ionic charge density distributions in nanopores. The effective medium approximation (EMA) participates in calculating the effective conductance and conductivity of the nanoscale HPM. The results show that the surface charge density af…
Liquid transport through nanopore is central into many applications, from water purification to biosensing or energy harvesting. Ultimately thin nanopores are of major interest in these applications to increase driving potential and reduce as much as possible dissipation sources. We investigate here the efficiency of the electrical power generation through an ultrathin nanoporous membrane by means of streaming current (electrical current induced by ionic flow in the vicinity of the liquid/solid interface) or electroosmosis (flow rate induced by an electrical potential). Upscaling from one uniq…
Observing finite regions of a bigger system is a common experience, from microscopy to molecular simulations. In the latter especially, there is ongoing interest in predicting thermodynamic properties from tracking fluctuations in finite observation volumes. However, kinetic properties have received less attention, especially not in ionic solutions, where electrostatic interactions play a decisive role. Here, we probe ionic fluctuations in finite volumes with Brownian dynamics and build an analytical framework that reproduces our simulation results and is broadly applicable to other systems wi…
A variational theory is developed to study electrolyte solutions, composed of interacting point-like ions in a solvent, in the presence of dielectric discontinuities and charges at the boundaries. Three important and non-linear electrostatic effects induced by these interfaces are taken into account: surface charge induced electrostatic field, solvation energies due to the ionic cloud, and image charge repulsion. Our variational equations thus go beyond the mean-field theory. The influence of salt concentration, ion valency, dielectric jumps, and surface charge is studied in two geometries. i)…
The influence of spatial confinement on the thermally excited stochastic cation dynamics of the room-temperature ionic liquid 1-N-butylpyridinium bis-((trifluoromethyl)sulfonyl)imide ([BuPy][Tf_2N]) inside porous carbide-derived carbons with various pore sizes in the sub- to a few nanometer range are investigated by quasi-elastic neutron spectroscopy. Using the potential of fixed window scans, i.e. scanning a sample parameter, while observing solely one specific energy transfer value, an overview of the dynamic landscape within a wide temperature range is obtained. It is shown that already the…
We develop a correlation-corrected transport theory in order to predict ionic and polymer transport properties of membrane nanopores in physical conditions where mean-field electrostatics breaks down. The experimentally observed low KCl conductivity of open alpha-Hemolysin pores is quantitatively explained by the presence of surface polarization effects. Upon the penetration of a DNA molecule into the pore, these polarization forces combined with the electroneutrality of DNA sets a lower boundary for the ionic current, explaining the weak salt dependence of blocked pore conductivities at dilut…
This work exploits the zeptoliter sensing volume of electrolyte-filled nanopores to determine, simultaneously and in real time, the approximate shape, volume, charge, rotational diffusion coefficient, and dipole moment of individual proteins. We have developed the theory for a quantitative understanding and analysis of modulations in ionic current that arise from rotational dynamics of single proteins as they move through the electric field inside a nanopore. The resulting multi-parametric information raises the possibility to characterize, identify, and quantify individual proteins and protei…
We study charge transport in an ionic solution in a confined nanoscale geometry in the presence of an externally applied electric field and immobile background charges. For a range of parameters, the ion current shows non-monotonic behavior as a function of the external ion concentration. For small applied electric field, the ion transport can be understood from simple analytic arguments, which are supported by Monte Carlo simulation. The results qualitatively explain measurements of ion current seen in a recent experiment on ion transport through a DNA-threaded nanopore (D. J. Bonthuis et. al…
